# Thread: Help with local max/min and global max/min

1. ## Help with local max/min and global max/min

I know how to solve for local min and max.

For instance,

F = 2x^2 + y^2 +4x -4y +5

The point (-1,2) is a local minimum, but my book also points out that it is a global minimum.

Can anyone tell me how to find the global max/min after I have found critical points and local max/min.

2. A global min is a point where the y-value is the least of all possible y-values in the range of the function. No other output will be less.

3. Originally Posted by messianic
I know how to solve for local min and max.

For instance,

F = 2x^2 + y^2 +4x -4y +5

The point (-1,2) is a local minimum, but my book also points out that it is a global minimum.

Can anyone tell me how to find the global max/min after I have found critical points and local max/min.
If you have found all the local minima, then (assuming the function doesn't go off to $- \infty$ at any point), the global minimum is the smallest of the local minima.

So what you need to do, to prove a global minimum, is show that it's the smallest of the local minima, and that the curve does not go off to $- \infty$.

Yes I know you weren't told to prove that it is a global minimum, consider this post a "for information" one.